TMA

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Calculation

Most implementations construct a triangular integer window over the time series.

A more effective and even more accurate algorithm uses a Bartlett window for construction. This kind of data window also has a triangular form but is based on floating point calculations.

Experimental Time Series

Real Time Series

C++-Source

inline double W_BARTLETT(double n, double k, double d = 1.0)
{
    return (n == 0) ? 0 : (d * (1 - fabs((k - 0.5 * n) / (0.5 * n))));
}

BOOL ivorix_tma (
          vector<double>& ivec,     // input  vector
          vector<double>& ovec,     // output vector
          unsigned long   span)     // time period or span of embedding
{
    ULONG   x     = 0;
    ULONG   y     = 0;
    ULONG   p     = 0;
    ULONG   e     = ivec.size();
    double  sum   = 0;
    double  div   = 0;

    if ( span == 0 || span >= e )
        return false;

    ovec.resize(ivec.size());

    ovec[0] = ivec[0];

    for ( x = 1; x < e; x++ )
    {
        sum = 0;
        p   = min(x, span);

        if ( p <= span )
        {
            div = 0;

            for ( y = 1; y <= p; y++ )
                div += W_BARTLETT(p+1, y, p);
        }

        for ( y = 1; y <= p; y++ )
            sum += ivec[x-y+1] * W_BARTLETT(p+1, y, p);

        ovec[x] = sum / div;
    }

    return true;
}

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